Problem: Rewrite as a simplified fraction. ${2.\overline{5} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 25.5555...\\ 1x &= 2.5555...\end{align*}}$ Subtracting the two equations, we have: ${9x = 23}$ ${x = \dfrac{23}{9}} \text{or} {2 \dfrac{5}{9}}$